diff --git a/NewKernel_d/include/CGAL/Kernel_d/Coaffine.h b/NewKernel_d/include/CGAL/Kernel_d/Coaffine.h
new file mode 100644
index 00000000000..2a95a7fb304
--- /dev/null
+++ b/NewKernel_d/include/CGAL/Kernel_d/Coaffine.h
@@ -0,0 +1,68 @@
+#ifndef CGAL_KD_COAFFINE_H
+#define CGAL_KD_COAFFINE_H
+#include <vector>
+// DRAFT, DOESN'T WORK YET
+namespace CGAL {
+struct Orientation_in_subspace {
+	std::vector<int> indices;
+	// use indices.size() to know if the origin is added
+	// an index of i means add the vector (0,...,1,...,0) with the 1 in i-th position
+	// *OR* it means *don't* add this one...
+};
+
+template<class R_> struct Construct_orientation_in_subspace : private Store_kernel<R_> {
+	CGAL_FUNCTOR_INIT_STORE(Construct_orientation_in_subspace)
+	typedef R_ R;
+	typedef typename R_::FT FT;
+	typedef typename R::template Type<Point_tag>::type Point;
+	typedef typename R::template Functor<Compute_cartesian_coordinate_tag>::type CCC;
+	typedef typename R::LA LA;
+	typedef typename LA::template Matrix<Dynamic_dimension,Dynamic_dimension,typename R::Max_ambient_dimension,typename R::Max_ambient_dimension>::type Matrix;
+	typedef typename R::template Functor<Point_dimension_tag>::type PD;
+	typedef Orientation_in_subspace result_type;
+
+	// This implementation is going to suck. Maybe we should push the
+	// functionality into LA.
+	template<class Iter>
+	result_type operator()(Iter f, Iter e)const{
+		PD pd (this->kernel());
+		CCC ccc (this->kernel());
+		int dim = pd(*f);
+		Matrix coord (dim, dim);
+		int col = 0;
+		std::vector<int> proj;
+		std::vector<int> rest; rest.reserve(dim);
+		for(int i=0; i<dim; ++i) rest.push_back(i);
+		for( ; f != e ; ++col, ++f ) {
+			Point const&p=*f;
+			for(int i=0; i<dim; ++i) coord(col, i) = ccc(p, i);
+			int d = proj.size()+1;
+			Matrix m (d, d);
+			// Fill the matrix with what we already have
+			for(int i=0; i<d; ++i)
+			for(int j=0; j<d-1; ++j)
+				m(i,j) = coord(i, proj[j]);
+			// Try to complete with any other coordinate
+			// TODO: iterate on rest by the end, or use a (forward_)list.
+			for(std::vector<int>::iterator it=rest.begin();it!=rest.end();++it) {
+				for(int i=0; i<d; ++i) m(i,d-1) = coord(i, *it);
+				if(LA::sign_of_determinant(m)==0) continue;
+				proj.push_back(*it);
+				rest.erase(it);
+			}
+			CGAL_assertion(it!=rest.end());
+		}
+		Orientation_in_subspace o;
+		// Check whether the origin is in the affine space (optimization)
+		int d = proj.size();
+		Matrix m (d+1, d+1);
+		// Mu ? J'ai ecrit le code pour des vecteurs au lieu de points :-(
+		for(int i=0; i<d; ++i)
+			for(int j=0; j<d-1; ++j)
+				m(i,j) = coord(i, proj[j]);
+		return o;
+	}
+};
+
+}
+#endif
diff --git a/NewKernel_d/include/CGAL/transforming_iterator.h b/NewKernel_d/include/CGAL/transforming_iterator.h
index ccc9d411db4..b4d398c5951 100644
--- a/NewKernel_d/include/CGAL/transforming_iterator.h
+++ b/NewKernel_d/include/CGAL/transforming_iterator.h
@@ -82,7 +82,7 @@ private internal::Functor_as_base<F>
 
 };
 
-template <typename F, typename Iter>
+template <typename F, typename Iter> inline
 transforming_iterator<F,Iter> make_transforming_iterator(Iter i, F const&f=F()) {
 	return transforming_iterator<F,Iter>(i,f);
 }
diff --git a/NewKernel_d/include/CGAL/transforming_pair_iterator.h b/NewKernel_d/include/CGAL/transforming_pair_iterator.h
index 72e6f6ac170..9df4b61c4e9 100644
--- a/NewKernel_d/include/CGAL/transforming_pair_iterator.h
+++ b/NewKernel_d/include/CGAL/transforming_pair_iterator.h
@@ -97,7 +97,7 @@ private internal::Functor_as_base<F>
 
 };
 
-template <typename F, typename It1, typename It2>
+template <typename F, typename It1, typename It2> inline
 transforming_pair_iterator<F,It1,It2> make_transforming_pair_iterator(It1 i1, It2 i2, F const&f=F()) {
 	return transforming_pair_iterator<F,It1,It2>(i1,i2,f);
 }